Indirect Magnetoelectric Coupling via Skew Scattering by Orbital Angular Momentum

Recent experimental observations of exchange bias in the La$_{0.67}$Sr$_{0.33}$MnO$_{3}$/LaAlO$_{3}$/SrTiO$_{3}$ heterostructure, which lacks an intrinsic antiferromagnetic layer, have sparked theoretical investigations into the underlying mechanisms. While traditional theories suggest that exchange bias in spin valve structures is mediated by conduction electrons in metallic spacers, the transport properties of LaAlO$3$ are dominated by its valence electrons, raising new questions about the origin of this phenomenon. In this work, we propose a theoretical model where the electronic band structure of LaAlO$_3$ is treated as a valence band perturbed by skew scattering, which is sensitive to orbital angular momentum. Our analysis reveals a significant magnetoelectric effect at the La$_{0.67}$Sr$_{0.33}$MnO$_3$/LaAlO$_3$ interface, which induces a coupling between the interface magnetization and the electric field from two dimensional electron gas at LaAlO$_{3}$/SrTiO$_{3}$ interface. This magnetoelectric coupling is found to drive the observed exchange bias, highlighting the role of electric polarization in influencing the magnetic properties of the heterostructure.